Robust passivity and passification of stochastic fuzzy time-delay systems

The official published version can be obtained from the link below.In this paper, the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time-varying delays. The fuzzy system is based on the Takagi–Sugeno (T–S) model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter uncertainties and the stochastic disturbances are considered, where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a Brownian motion. We first propose the definition of robust passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the Itô differential rule and the matrix analysis techniques, we establish several sufficient criteria such that, for all admissible parameter uncertainties and stochastic disturbances, the closed-loop stochastic fuzzy time-delay system is robustly passive in the sense of expectation. The derived criteria, which are either delay-independent or delay-dependent, are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.This work was supported by the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers 200802861044, the National Natural Science Foundation of China under Grant 60804028 and the Royal Society of the United Kingdom

ROBUST STABILIZATION AND OPTIMIZATION OF FLIGHT CONTROL SYSTEM WITH STATE FEEDBACK AND FUZZY LOGICS

This paper deals with combination of two powerful and modern control tools as linear matrix inequality that is used for synthesis a ‘crisp’ controller and a fuzzy control approach for designing a soft controller. The control design consists of two stages. The first stage investigates the problem of a robust an H2 controller design with parameters uncertainties of the handled plant in the presence of external disturbances. Stability onditions are obtained via a quadratic Lyapunov function and represented in the form of linear matrix inequalities. The second stage consists of the outer loop controller construction based on fuzzy inference system that utilizes for altitude hold mode. The parameters of the fuzzy controller are adjusted with a gradient descent method in order to improve the performance of the overall system. The case study illustrates the efficiency of the proposed approach to the flight control of small Unmanned Aerial Vehicle.Розглянуто принцип поєднання двох потужних та сучасних засобів теорії управління як метод лінійних матричних нерівностей, який використовується для синтезу чіткого регулятора та нечіткого управління для синтезу регулятора з м’якими обчисленнями. Процедура синтезу складається з двох етапів. На першому етапі вирішено задачу синтезу робастного H2 - регулятора для безпілотного літального апарату із врахуванням зовнішніх збурень, які діють на об’єкт управління. Умови стійкості сформовано у вигляді лінійних матричних нерівностей. Другий етап присвячено задачі синтезу нечіткого регулятора для зовнішнього контуру управління в режимі стабілізації висоти, заснованого на нечіткій логіці. З метою покращення якості управління параметри нечіткого регулятора настроюються за допомогою градієнтного методу. Проведено дослідження на прикладі управління поздовжнім каналом безпілотного літального апарату

Stabilisation robuste des systèmes Takagi-Sugeno par lois de commande à commutations

International audienceDans cet article, la stabilisation des systèmes non linéaires incertains et perturbés est abordée à travers une modélisation sous forme de modèles flous de type Takagi-Sugeno (T-S) à commutations. Afin d'assurer la stabilisation robuste des systèmes T-S incertains et perturbés à commutations garantissant la minimisation de l'effet des perturbations externes, une méthodologie de synthèse quadratique H∞ de lois de commande floues à commutations est proposée. Les conditions de stabilité sont exprimées en termes d'Inégalités Linéaires Matricielles (LMI). Finalement, un exemple numérique illustre l'efficacité de l'approche proposée

State constrained tracking control for nonlinear systems

Abstract This work addresses the model reference tracking control problem. It aims to highlight the encountered difficulties and the proposed solutions to achieve the tracking objective. Based on a literature overview of linear and nonlinear reference tracking, the achievements and the limitations of the existing strategies are highlighted. This motivates the present work to propose clear control algorithms for perfect and approximate tracking controls of nonlinear systems described by Takagi-Sugeno models. First, perfect nonlinear tracking control is addressed and necessary structural conditions are stated. If these conditions do not hold, approximate tracking control is proposed and the choice of the reference model to be tracked as well as the choice of the criterion to be minimized are discussed with respect to the desired objectives. The case of constrained control input is also considered in order to anticipate and counteract the effect of the control saturation

Active fault-tolerant control of nonlinear systems with wind turbine application

The thesis concerns the theoretical development of Active Fault-Tolerant Control (AFTC) methods for nonlinear system via T-S multiple-modelling approach. The thesis adopted the estimation and compensation approach to AFTC within a tracking control framework. In this framework, the thesis considers several approaches to robust T-S fuzzy control and T-S fuzzy estimation: T-S fuzzy proportional multiple integral observer (PMIO); T-S fuzzy proportional-proportional integral observer (PPIO); T-S fuzzy virtual sensor (VS) based AFTC; T-S fuzzy Dynamic Output Feedback Control TSDOFC; T-S observer-based feedback control; Sliding Mode Control (SMC). The theoretical concepts have been applied to an offshore wind turbine (OWT) application study. The key developments that present in this thesis are:• The development of three active Fault Tolerant Tracking Control (FTTC) strategies for nonlinear systems described via T-S fuzzy inference modelling. The proposals combine the use of Linear Reference Model Fuzzy Control (LRMFC) with either the estimation and compensation concept or the control reconfiguration concept.• The development of T-S fuzzy observer-based state estimate fuzzy control strategy for nonlinear systems. The developed strategy has the capability to tolerate simultaneous actuator and sensor faults within tracking and regulating control framework. Additionally, a proposal to recover the Separation Principle has also been developed via the use of TSDOFC within the FTTC framework.• The proposals of two FTTC strategies based on the estimation and compensation concept for sustainable OWTs control. The proposals have introduced a significant attribute to the literature of sustainable OWTs control via (1) Obviating the need for Fault Detection and Diagnosis (FDD) unit, (2) Providing useful information to evaluate fault severity via the fault estimation signals.• The development of FTTC architecture for OWTs that combines the use of TSDOFC and a form of cascaded observers (cascaded analytical redundancy). This architecture is proposed in order to ensure the robustness of both the TSDOFC and the EWS estimator against the generator and rotor speed sensor faults.• A sliding mode baseline controller has been proposed within three FTTC strategies for sustainable OWTs control. The proposals utilise the inherent robustness of the SMC to tolerate some matched faults without the need for analytical redundancy. Following this, the combination of SMC and estimation and compensation framework proposed to ensure the close-loop system robustness to various faults.• Within the framework of the developed T-S fuzzy based FTTC strategies, a new perspective to reduce the T-S fuzzy control design conservatism problem has been proposed via the use of different control techniques that demand less design constraints. Moreover, within the SMC based FTTC, an investigation is given to demonstrate the SMC robustness against a wider than usual set of faults is enhanced via designing the sliding surface with minimum dimension of the feedback signals

Output feedback LMI tracking control conditions with H∞ criterion for uncertain and disturbed TS models

International audienceThis work concerns the tracking problem of uncertain Takagi-Sugeno (T-S) continuous fuzzy model with external disturbances. The objective is to get a model reference based output feedback tracking control law. The control scheme is based on a PDC structure, a fuzzy observer and a H∞ performance to attenuate the external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key point of the proposed approaches is to achieve conditions under a LMI (linear matrix inequalities) formulation in the case of an uncertain and disturbed T-S fuzzy model. This formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems. Finally, a simulation is provided on the well-known inverted pendulum testbed to show the efficiency of the proposed approach

An Lmi-based Approach To Static Output Feedback Stabilization Of T-s Fuzzy Systems

The problem of static output feedback control design for continuous-time Takagi- Sugeno (T-S) fuzzy systems is addressed in this paper. The membership functions are modeled in a space defined by the Cartesian product of simplexes, called multi-simplex, and are allowed to vary arbitrarily (i.e. no bounds on the time-derivative of the membership functions are assumed). The static output feedback fuzzy controller is obtained through a two-step procedure: first, a stabilizing fuzzy state feedback control gain is determined by means of linear matrix inequalities (LMIs). Then, the state feedback gain matrices are used in LMI conditions that, if satisfied, provide the fuzzy static output feedback control law. A fuzzy line integral Lyapunov function with arbitrary polynomial dependence on the premise variables is used to assess closedloop stability. The main appeal of the approach is that the output feedback gains can have independent and arbitrary polynomial dependence on some specific premise variables, selected by the designer, with great advantages for practical applications. An example illustrates that the proposed strategy can provide less conservative results when compared to other methods from the literature for output feedback stabilization of continuous-time T-S fuzzy systems. © 2011 IFAC.18PART 11259312598Agulhari, C.M., Oliveira, R.C.L.F., Peres, P.L.D., Robust H ∞ static output-feedback design for time-invariant discrete-time polytopic systems from parameter-dependent state-feedback gains (2010) Proceedings of the 2010 American Control Conference, pp. 4677-4682. , Baltimore, MD, USA, June-JulyArzelier, D., Peaucelle, D., An iterative method for mixed H 2/H ∞ synthesis via static output-feedback (2002) Proceedings of the 41st IEEE Conference on Decision and Control, pp. 3464-3469. , Las Vegas, NV, USA, DecemberArzelier, D., Peaucelle, D., Salhi, S., Robust static output feedback stabilization for polytopic uncertain systems: Improving the guaranteed performance bound (2003) Proceedings of the 4th IFAC Symposium on Robust Control Design (ROCOND 2003), , Milan, Italy, JuneArzelier, D., Gryazina, E.N., Peaucelle, D., Polyak, B.T., Mixed LMI/Randomized methods for static output feedback control design (2010) Proceedings of the 2010 American Control Conference, pp. 4683-4688. , Baltimore, MD, USA, June-JulyBaranyi, P., TP model transformation as a way to LMIbased controller design (2004) IEEE Transactions on Industrial Electronics, 51 (2), pp. 387-400. , AprilBouarar, T., Guelton, K., Manamanni, N., Static output feedback controller design for Takagi-Sugeno systems - A fuzzy Lyapunov LMI approach (2009) Proceedings of the 48th IEEE Conference on Decision and Control - 28th Chinese Control Conference, pp. 4150-4155. , Shanghai, P. R. China, DecemberFang, C.-H., Liu, Y.-S., Kau, S.-W., Hong, L., Lee, C.-H., A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems (2006) IEEE Transactions on Fuzzy Systems, 14 (3), pp. 386-397. , JuneGuelton, K., Bouarar, T., Manamanni, N., Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi-Sugeno systems - A descriptor redundancy approach (2009) Fuzzy Sets and Systems, 160 (19), pp. 2796-2811. , OctoberGuerra, T.M., Kruszewski, A., Vermeiren, L., Tirmant, H., Conditions of output stabilization for nonlinear models in the Takagi-Sugeno's form (2006) Fuzzy Sets and Systems, 157 (17), pp. 1248-1259. , MayHuang, D., Nguang, S.K., Static output feedback controller design for fuzzy systems: An ILMI approach (2007) Information Sciences, 177 (14), pp. 3005-3015. , JulyLee, H.J., Kim, D.W., Fuzzy static output feedback may be possible in LMI framework (2009) IEEE Transactions on Fuzzy Systems, 17 (5), pp. 1229-1230. , OctoberMansouri, B., Manamanni, N., Guelton, K., Kruszewski, A., Guerra, T.M., Output feedback LMI tracking control conditions with H ∞ criterion for uncertain and disturbed T-S models (2009) Information Sciences, 179 (4), pp. 446-457. , FebruaryMehdi, D., Boukas, E.K., Bachelier, O., Static output feedback design for uncertain linear discrete time systems (2004) IMA Journal of Mathematical Control and Information, 21 (1), pp. 1-13. , MarchMozelli, L.A., Palhares, R.M., Avellar, G.S.C., A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems (2009) Information Sciences, 179 (8), pp. 1149-1162. , MarchMozelli, L.A., Palhares, R.M., Souza, F.O., Mendes, E.M.A.M., Reducing conservativeness in recent stability conditions of TS fuzzy systems (2009) Automatica, 45 (6), pp. 1580-1583. , JuneNguang, S.K., Shi, P., Robust H ∞ output feedback control design for fuzzy dynamic systems with quadratic D stability constraints: An LMI approach (2006) Information Sciences, 176 (15), pp. 2161-2191. , AugustPeaucelle, D., Arzelier, D., An efficient numerical solution for H 2 static output feedback synthesis (2001) Proceedings of the 2001 European Control Conference, , Porto, Portugal, SeptemberRhee, B.-J., Won, S., A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design (2006) Fuzzy Sets and Systems, 157 (9), pp. 1211-1228. , MaySyrmos, V.L., Abdallah, C.T., Dorato, P., Grigoriadis, K., Static output feedback - A survey (1997) Automatica, 33 (2), pp. 125-137. , FebruaryTakagi, T., Sugeno, M., Fuzzy identification of systems and its applications to modeling and control (1985) IEEE Transactions on Systems, Man, and Cybernetics, SMC-15 (1), pp. 116-132. , JanuaryTanaka, K., Hori, T., Wang, H.O., A fuzzy Lyapunov approach to fuzzy control system design (2001) Proceedings of the 2001 American Control Conference, pp. 4790-4795. , Arlington, VA, USA, JuneTanaka, K., Hori, T., Wang, H.O., A multiple Lyapunov function approach to stabilization of fuzzy control systems (2003) IEEE Transactions on Fuzzy Systems, 11 (4), pp. 582-589. , AugustTognetti, E.S., Oliveira, R.C.L.F., Peres, P.L.D., Selective stabilization of Takagi-Sugeno fuzzy systems (2010) Proceedings of the 2010 IEEE International Conference on Fuzzy Systems, pp. 2772-2779. , Barcelona, Spain, Jul